{"id":"W4362632869","doi":"10.1017/etds.2023.18","title":"Direct and inverse results for popular differences in trees of positive dimension","year":2023,"lang":"en","type":"article","venue":"Ergodic Theory and Dynamical Systems","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"University of Sydney; Stanley Medical Research Institute","keywords":"Ergodic theory; Mathematics; Inverse; Measure (data warehouse); Type (biology); Dimension (graph theory); Extension (predicate logic); Tree (set theory); Set (abstract data type); Markov chain; Stability (learning theory); Combinatorics; Discrete mathematics; Pure mathematics; Statistics; Data mining; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002233879,0.0003323098,0.001037048,0.003518729,0.001746643,0.003567375,0.001397628,0.0009974317,0.005780046],"category_scores_gemma":[0.01315251,0.0005559646,0.0008851498,0.00181995,0.004191156,0.006484163,0.003265385,0.002168225,0.0003853725],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001533518,"about_ca_system_score_gemma":0.0003381967,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006443894,"about_ca_topic_score_gemma":0.0006647491,"domain_scores_codex":[0.9983466,0.0003412894,0.0001020186,0.0004128779,0.0006289131,0.0001683568],"domain_scores_gemma":[0.9861001,0.009758662,0.001128724,0.0008176198,0.001273099,0.0009217168],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003126314,0.00003341641,0.002139261,0.00007252259,0.00001510036,0.00007947877,0.0004493539,0.002848944,0.001049595,0.9885401,0.0004101266,0.004330873],"study_design_scores_gemma":[0.00001541248,0.00003439396,0.002388365,0.00003126274,0.00001939974,0.0005134007,0.0003417611,0.02763837,0.001416025,0.9641834,0.003392419,0.00002575785],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6406704,0.001424687,0.3159706,0.001084385,0.00008241783,0.00007005184,0.0005807179,0.0001982888,0.03991854],"genre_scores_gemma":[0.9828914,0.00039871,0.01302221,0.0001562192,0.0001308359,0.00007085768,0.0002266415,0.00004355618,0.003059391],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005780046,"threshold_uncertainty_score":0.01933616,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02125799359740817,"score_gpt":0.2698615910068015,"score_spread":0.2486035974093933,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}